Global dynamics of a Lotka-Volterra system in ℝ³

In this work we consider the Lotka-Volterra system in R³ x˙ = −x(x − y − z), y˙ = −y(−x + y − z), z˙ = −z(−x − y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they studied the system as a Hamilton-Poisson system, and also started the analysis of its dynamics. Here we provide the global phase portraits of this 3-dimensional Lotka-Volterra system in the Poincaré ball, that is in R³ adding its extension to the infinity